Question

jayla is making dog toys for the helping heart animal rescue using rope donated by a local hardware store. as she cuts sections of rope to form into knots, the amount of donated rope she has left decreases. this situation can be modeled as a linear relationship. chart: x-axis: dog toys made (0 - 20), y-axis: rope left (feet) (50 - 500). line starts at (0, 400) and ends at (20, 80? or similar, with grid). complete the statement that describes the situation. jayla starts with blank feet of donated rope. she uses blank feet of rope for each dog toy.

Explanation:

Step1: Find the initial amount of rope

The y - intercept of the linear graph represents the initial amount of rope (when \(x = 0\), i.e., when no dog toys are made). From the graph, when \(x=0\), \(y = 400\). So Jayla starts with 400 feet of rope.

Step2: Calculate the slope (amount of rope per toy)

The slope \(m\) of a line is given by \(\frac{y_2 - y_1}{x_2 - x_1}\). We can use two points, say \((0,400)\) and \((20,80)\) (from the graph, when \(x = 20\), \(y=80\)).
\(m=\frac{80 - 400}{20-0}=\frac{- 320}{20}=- 16\). The negative sign indicates a decrease, and the absolute value 16 is the amount of rope used per dog toy.

Answer:

Jayla starts with \(\boldsymbol{400}\) feet of donated rope. She uses \(\boldsymbol{16}\) feet of rope for each dog toy.